Anomalies are unsuitable measure of global temperature trends
Guest post by David M. Hoffer
An anomaly is simply a value that is arrived at by comparing the current measurement to some average measurement. So, if the average temperature over the last 30 years is 15 degrees C, and this year’s average is 16 degrees, that gives us an anomaly of one degree. Of what value are anomalies? Are they a suitable method for discussing temperature data as it applies to the climate debate?
On the surface, anomalies seem to have some use. But the answer to the second question is rather simple.
No.
If the whole earth was a single uniform temperature, we’d have no need of anomalies. But the fact is that temperatures don’t vary all that much in the tropics, while variations in the high temperate zones are frequently as much as 80 degrees over the course of a year. How does one compare the temperatures of say Khartoum, which on a monthly basis ranges from an average of 25 degrees to 35 degrees C, to say Winnipeg, which might range from -40 in the winter to +40 in the summer?
Enter anomalies. By establishing a base line average, usually over 30 years, it is possible to see how much temperatures have changed in (for example) winter in Winnipeg Canada versus Khartoum in summer. On the surface, this makes sense. But does the physics itself support this method of comparison?
It absolutely does NOT.
The theory of CO2’s direct effects on earth’s surface temperature is not terribly difficult to understand. For the purposes of this discussion, let us ignore the details of the exact physical mechanisms as well as the order and magnitude of feedback responses. Let us instead assume that the IPCC and other warmist literature is correct on that matter, and then see if it is logical to analyze that theory via anomaly data.
The “consensus” literature proposes that direct effects of CO2 result in a downward energy flux of 3.7 watts/m2 for a doubling of CO2. Let’s accept that. Then they propose that this in turn results in a temperature increase of one degree. That proposal cannot be supported.
Let us start with the one degree calculation itself. How do we convert watts/m2 into degrees?
The answer can be found in any text book that deals with radiative physics. The derivation of the formula requires some in depth understanding of the matter, and for those that are interested, Wikipedia has as good an explanation as we need:
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
For the purposes of this discussion however, all we need to understand is the formula itself, which is:
P=5.67*10^-8*T^4
It took Nobel Prize winning work in physics to come up with that formula, but all we need to use it is a calculator.
For the mathematically inclined, the problem ought to be immediately obvious. There is no direct correlation between w/m2 and temperature. Power varies with T raised to the power of 4. That brings up an obvious question. At what temperature does the doubling of CO2 cause a rise in temperature of one degree? If we use the accepted average temperature of earth surface as +15 degrees C (288 degrees K) simply applying the formula suggests that it is NOT at the average surface temperature of earth:
For T = 288K
P = 5.67*10^-8*288^4 = 390.1
For T = 289K (plus one degree)
P = 5.67*10^-8*289^4 = 395.5
That’s a difference of 5.4 w/m2, not 3.7 w/m2!
So, how does the IPCC justify their claim? As seen from space, the earth’s temperature is not defined at earth surface, nor can it be defined at the TOA (Top of Atmosphere). Photons escaping from earth to space can originate at any altitude, and it is the average of these that defines the “effective black body temperature of earth” which turns out to be about -20 C (253 K), much colder than average temperatures at earth surface. If we plug that value into the equation we get:
253K = 232.3 w/m2
254K = 236.0 w/m2
236.0 – 232.3 = 3.7
There’s the elusive 3.7 w/m2 = 1 degree! It has nothing to do with surface temperatures! But if we take this analysis a step further, it gets even worse. The purpose of temperature anomalies in the first place was supposedly to compare temperature changes at different temperature ranges. As we can see from the analysis above, since w/m2 means very different things at different temperature ranges, this method is completely useless for understanding changes in earth’s energy balance due to doubling of CO2.
To illustrate the point further, at any given time, some parts of earth are actually in cooling trends while others are in warming trends. By averaging temperature anomalies across the globe, the IPCC and “consensus” science has concluded that there is an overall positive warming trend. The following is a simple example of how easily anomaly data can report not only a misleading result, but worse, in some cases it can report a result the OPPOSITE of what is happening from an energy balance perspective. To illustrate, let’s take four different temperatures and consider their value when converted to w/m2 as calculated by Stefan-Boltzmann Law:
-38 C = 235K = 172.9 w/m2
-40 C = 233K = 167.1 w/m2
+35 C = 318K = 579.8 w/m2
+34 C = 317K = 587.1 w/m2
Now let us suppose that we have two equal areas, one of which has an anomaly of +2 due to warming from -40 C to -38 C. The other area at the same time posts an anomaly of -1 due to cooling from +35 to +34.
-38 C anomaly of +2 degrees = +5.8 w.m2
+35 C anomaly of -1 degree = -7.3 w/m2
“averaged” temperature anomaly = +0.5 degrees
“averaged” w/m2 anomaly = -0.75 w.m2
The temperature went up but the energy balance went down? The fact is that because temperature and power do not vary dirfectly with one another, averaging anomaly data from dramaticaly different temperature ranges provides a meaningless result.
Long story short, if the goal of measuring temperature anomalies is to try and quantify the effects of CO2 doubling on earth’s energy balance at surface, anomalies from winter in Winnipeg and summer in Khartoum simply are not comparable. Trying to average them and draw conclusions about CO2’s effects in w/m2 simply makes no sense and produces a global anomaly that is meaningless.
Anomalies are just the best, least biased, most objective and most comparable method for averaging temperature over time and space, whether it be for a state, country or planet. The goal of using anomalies is to compare changes, not to say how or why they occurred. So, i don’t understand how a critique of anomalies is related to CO2 (or possibly, sun spots). If we are going to talk about climate, it’s importantl to be able to quantify whether factors such as temperature and precipitation are increasing or decreasing over a region or even the whole planet. Rather than giving up on studying climate, we use anomalies. If you really believe that calculating anomalies are a problem, then describe an alternative.
BillD says:
August 28, 2012 at 1:26 pm
It the baseline that is the problem, not the anomalies. I tried to simplify it so that everyone could understand what is meant by anomaly ( in climate science ), but apparently it has served to confuse.
Lord Monckton,
I am not that sure that the IPCC adjustments for anomalies are adequate. If the AQUA sea surface data is correct, the average true temperature of ~70% of the Earth’s surface is approximately 21.1 C, 294.25K with a S-B equivalent radiant energy of 425Wm-2. The revised surface energy estimate is 396Wm-2. That would require a fairly large adjustment for the use of anomalies on land especially at a higher average elevation.
Since the models started diverging circa 1995 when the northern oceans reach a relative equilibrium with the southern oceans, that could explain a large portion of the error. It is at least worth looking into more closely.
And 1951-1980 choice of baseline appears to be the worst possible now that there is satellite data to use.
http://redneckphysics.blogspot.com/2012/08/degrees-of-confusion-another-modest.html
BillD;
So, i don’t understand how a critique of anomalies is related to CO2
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CO2’s effects are measured in w/m2, not degrees. There needs to be a mechanism to convert between the two in order to measure actual effects versus theorized effects. The point of this thread is that there is no straight forward conversion between the two.
It “is” the baseline, of course.
BillD nailed this threat when on
August 28, 2012 at 1:26 pm, he said:
“Anomalies are just the best, least biased, most objective and most comparable method for averaging temperature over time and space, whether it be for a state, country or planet. The goal of using anomalies is to compare changes, not to say how or why they occurred.”
A little bit of common sense sure does go a long way and I hope that we continue to report good old temperatures at places X, Y, and Z – as well as average temperatures at places X, Y and Z – as well as record temperatures at points X, Y, and Z – as well as all of the above averaged over the entire planet, if possible.
ricgrimsrud says:
August 28, 2012 at 8:41 am
Sorry, but I still do have the impression that a measurement of the average global temperature and changes in it over time is of considerable value and even of primary importance….
I am getting the feeling that a purpose of this threat is to diminish the perceived importance of simple, credible and easily understood surface temperature measurements – in favor of more obtuse measurements along with heavy doses of theory. Sorry, but when I think I might be running a fever, I will get out my theromometer first – before heading for the journals of medicine.
____________________________
I thought you were a chemist and therefore should understand enthalpy and the concept of measuring the correct parameter.
Here is an easy real life example.
1.) If I want to figure out the maximum weight a horse/pony can carry do I just measure the height? (easy)
2.) Do I look at the circumference of the cannon bone, the length of the back, weight and the age of the animal? (correct)
I have animals that are tall and have long weak backs that can not carry near the weight my short coupled, big boned stocky Shetland can. Given the ponies with weak backs will bite, balk or buck the incorrect analysis has fast feedback. Too bad “Climate Scientists” don’t get bitten in the rear when they make stupid mistakes.
(I am a chemist who finally quit in disgust after being asked to falsify data one too many times.)
BillD says:
August 28, 2012 at 1:26 pm
If you really believe that calculating anomalies are a problem, then describe an alternative.
My understanding is that there are two huge problems with anomalies:
1. The humidity has a huge affect on the total heat but is not accounted for and
2. There is a difference in the amount of heat it takes to heat something from -40 to -39 than from +40 to +41.
One way to get around the first problem is to just use the sea surface temperatures and not land temperatures. In case you are wondering what the sea surface temperatures show, it is that there has been no warming since January 1997, exactly what RSS shows. See:
http://www.woodfortrees.org/plot/rss/from:1997/plot/rss/from:1997/trend/plot/hadsst2gl/from:1997/plot/hadsst2gl/from:1997/trend
I just want to say thank you David. I am amazed that you point about temperature being an unsuitable parameter is actually contested. It makes me think the calculations have been done correctly and they show information the IPCC would rather the public at large does not know, otherwise why fight the point?
A little bit of common sense sure does go a long way and I hope that we continue to report good old temperatures at places X, Y, and Z – as well as average temperatures at places X, Y and Z – as well as record temperatures at points X, Y, and Z – as well as all of the above averaged over the entire planet, if possible.
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Who the heck said ANYTHING about not recording them? The entire thread is about using the information derived from them correctly.
Gail Combs;
It makes me think the calculations have been done correctly and they show information the IPCC would rather the public at large does not know, otherwise why fight the point?
>>>>>>>>>>>>
Well, I think that for the models themselves, they probably are handled correctly. Monckton of Brenchley certainly seems to think so. I’ll be looking into it myself to see exactly how they handle it, but if Monckton said the sky had turned purple with flourescent polka dots, I’d go outside and look for myself before disputing him, so I’m taking his word for it at the moment. Temperature trends like those presented by NASA/GISS and HadCrut on the other hand are simple area waited averages. They don’t take into account SB Law nor humidity, so are of little value in my mind to quantifyenergy balance. Nor do they take into account heat of transition, so all that ice that is melting in the arctic and being created in the antarctic also skew the numbers and aren’t picked up in any way by simple temperature trending.
That said, I don’t see a deliberate attempt to manipulate the numbers in this regard. I’m a big fan of never attributing to malice what can be explained by incompetance.
@ericgrimsrud,
Yes, a single figure for the average temperature of the surface land mass is simple and easy to use, but, as the precise details of the planet warms and cools is being worked out, it does not help understanding these mechanisms if the main measure, average temp, is wholly unsuitable for the obvious reasons given earlier.
The crux is: define the power flow to/from the earth, and what influences it. Is it CO2, other gases, clouds driven by particles or what?
There are are 1001 parameters that influence power flows to/from the earth. Each one needs to be understood.
Power flows are the key to understanding the mechanisms of earth climate.
Average temperatures are a poor proxy for power flow…
This thread has become significant.
To Ericgrimsrud
I am not sure that you really understood what is criticised here. In the original post but mostly in the comments.
Of course no sane person denies the EXISTENCE of an average. Of any average.
You have N numbers? Just add them up and divide the result by N. Here you go. Works for people’s weights, tomatoe diameters, temperatures. Any list of numbers you want. Trivial and uninteresting in most cases.
The point is this your statement :
Sorry, but I still do have the impression that a measurement of the average global temperature and changes in it over time is of considerable value and even of primary importance.
And as it has been abundantly demonstrated here, including in my post, this statement is obviously wrong.
So again I will give a list of questions on which the global temperature average and its variations does NOT answer, can NOT answer and even worse, can mislead to give wrong answers.
– The value of the internal energy and the sign of its variation
– The value of radiation flow and the sign of its variation. Not even its average.
– The value of the convective heat transfer and the sign of its variation. Not even its average
– The value of humidity and the sign of its variation. Not even its average. Here just for fun, the following statement may be true :”The average temperature increased and the average humidity decreased”.
– And more.
Science is science because it can lead to correct predictions, preferably about the future.
Because the global temperature average and its variations can not aswer the questions above, it can lead to absolutely NO prediction. Amusingly not even to its own.
So how do you call a parameter which is useless, misleading and irrelevant to anything that is important ?
Well about every scientist will call it garbage.
You apparently call it a parameter “of primary importance” what is exactly the opposite and of course obviously wrong.
And the reason why it is garbage is precisely because a given global temperature average corresponds to an infinity of dynamical states and to an infinity of possible evolutions that mutually contradict themselves both in value and in sign.
The only possible use of a global average is a tautological inferrence “If the global temperature average increased/decreased then T2 is greater/smaller than T1”.
I hope you agree that this inferrence is trivial, quite stupid and with no added value.
dallas says: August 28, 2012 at 5:23 pm
And 1951-1980 choice of baseline appears to be the worst possible now that there is satellite data to use.
Please check this plot using numerous different baseline dates. It should be obvious that there is no change in slope (or wiggles). The only change is in offset from zero for each baseline.
This makes no difference when considering how much the world has cooled/warmed from 1965 to 2012 All those different baselines will come up with the same result.
http://tinyurl.com/buk8e24
sergimk, “This makes no difference when considering how much the world has cooled/warmed from 1965 to 2012 All those different baselines will come up with the same result.”
True, there would be no difference in the amount the world has warmed or cooled by changing the baseline of the already averaged GMT, but it would make a difference as to what is suspected of causing the warming or cooling when the individual regions are compared with different base lines as I did in the link. For example in the 1940s, there is an abrupt drop in temperature in the tropics then a steady decline in temperature in the northern hemisphere. Is that consistent with man made aerosol cooling? Since the amplitude of the NH swing is so much larger than the rest of the world, selecting a baseline period where the NH is in a valley would show a larger increase in temperature than would be shown be selecting a neutral portion of the NH swing. The 1951 to 1980 baseline selection indicates more warming than a 1931-1960 baseline.
So I would think it would be worth the effort to determine what should be normal before declaring how abnormal things are.
I think that changes in temperature and precipitation are important to know and that anomalies are the best way of comparing and quantifying these changes. As a scientist, I say that the “baseline” is abitrary, but that it should not be frequently changed, since that makes comparisons confusing. It’s also better if everyone uses the same baseline, so that we are confused by anomalies that differ because the basedline is different. Measuring changes in radiative forcing (Watts/m2), water temperature and humidity can all help in our understanding of climate. However, we don’t need to answer all questions at once. Climate and weather are complicated so we will never find a single number that explains everything.
BillD, Using a consistent baseline would be nice. Since the satellite period limits what can be used as a baseline, what do you do?
http://redneckphysics.blogspot.com/2012/08/baseline-impact.html
It does matter as far as visual impact and the further the anomaly values vary from the baseline the greater the potential error.
Then the downside of a consistent baseline would be limiting the fun of cherry picking 🙂
OK, so would those of you who say that average global surface temperatures are meaningless and that the anomalies thereby observed are nothing more than “anoma-lies” please suggest a measure that would replace those simple and readily understood temperature measurements?
Now let me also guess here what that suggestion is likely to be – if anything meaningful can be envisioned. It will surely be something very complex that the public (as well as many scientists) would not be able to understand and would be subject to determination by a combinations of measurements and theory. Because of its uncertainty and large error bars, it too could then be considered by the AGW contrarians to be of little practical value!! Mission accomplished – we then would no longer have any measurement that reliably tells us whether the Earth’s temperature is changing !!! And all this is possible if the contrarians can just get those damn temperature measurements off the table.
Excuse me once more, but there seems to be something fishy behind this post.
ericgrimsrud says:
“…contrarians …contrarians…”
Exactly what is that label supposed to mean? The fact is that everything we observe today is fully explained by natural climate variability. That is the default position; the null hypothesis.
Attempting to impute extraneous variables as the cause of entirely natural fluctuations violates Occam’s Razor. To throw an unnecessary variable like “carbon” into the explanation of natural variability only muddies the waters, and leads to a wrong conclusion. Thus, it is you who is a ‘contrarian’. You believe you see things that are just not there. You are only fooling yourself – the easiest person in the world to fool.
Smokey
Eric Grimsrud is not fooling himself. He is fully aware of what he is doing. He and his band of fanatics are specifically out to fool others with this AGW scam, especially innocent people, with deliberate intent. Don’t assume that these people are innocent and are honest.
ericgrimsrud says:
August 29, 2012 at 7:56 am
It is fishy because you are clearly trying to misunderstand. Judging from your posts, I cannot figure out if it is on purpose, or through ineptitude. After reading all your posts, I have come to the conclusion it is the latter, ….
“A little bit of common sense sure does go a long way and I hope that we continue to report good old temperatures at places X, Y, and Z – as well as average temperatures at places X, Y and Z – as well as record temperatures at points X, Y, and Z – as well as all of the above averaged over the entire planet, if possible.”
Have you even read Anthony’s paper? Are you also aware that there are approximately 4000 less monitoring stations than there were 40 years ago? Check out The Chiefio – E.M. Smith. Your knowledge about this issue is sorely lacking.
Venter says:
August 29, 2012 at 8:18 am
I agree wholeheartedly. However, there are thousands of “lurkers” who frequent this site. I post stuff for people like ericgrimsrud, knowing full well that he will NOT read it, but many lurkers who are interested in learning ALL about this subject, will. I believe David M Hoffer posts a lot for this very reason. It is why Anthony has ALL the weather and sun data on his sidebar. Even some that may conflict with our presumptions. THAT is science. We have the courage to face and seek out ALL the information. What ericgrimsrud is doing is politics, not science.
ericgrimsrud;
Excuse me once more, but there seems to be something fishy behind this post.
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That’s the best you can do Eric? It seems fishy? You cannot dispute the factual information provided, so you call it fishy? Sit back Eric and think for a moment as to what that says, not about the science being discussed in this thread, but what it says about you. As for your question as to what should “replace” temperature, it should be obvious from the extensive discussion that temperature CANNOT be replaced, but that there are appropriate ways of handling and interpreting that temperature data. There have been several explanations in this discussion. What value is there in asking me to provide an alternative and belittling it before I provide it when perfectly viable alternatives have already been posted in this thread and which you are free to comment on? Why is it that in each and every thread in which we converse, it ends this same way, with you throwing around comments like “it seems fishy” and failing to actually engage in the discussion of facts and science itself? Do you have a PhD in Chemistry or not? If so, then I suggest you start acting like it.
ALL
I’m unlikely to respond further to Eric Grimsrud until he grows up and engages in the discussion like the adult with a PhD in Chemistry that he claims to be. Over the course of the last few weeks and across several threads, he has accused Anthony of taking money from “Big Oil”, he has accused me of taking money from Anthony for the purpose of poisoning the science, he has engaged in repeated ad hominem attacks including calling both richardscourtney and me “feces” and is a self proclaimed sock puppet for the Union of Concerned Scientists.
ericgrimsrud says:
August 29, 2012 at 7:56 am
Excuse me once more, but there seems to be something fishy behind this post.
If the earth had warmed up from something like 15 C to the temperature of Venus, then I would agree with you. However it is presumed that a warming of only 0.7 C occurred in the last 150 years. And when you factor in how much of this 0.7 C is due to faulty weather stations, the UHI effect, thermometers disappearing, and the warming of extremely dry and cold air in the north polar region and how GISS handles it, then it is a very legitimate question to ask how much energy the earth really gained over the last 150 years.